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A228300
Composite squarefree numbers n such that p-d(n) divides n-d(n), where p are the prime factors of n and d(n) the number of divisors of n.
5
6, 10, 15, 110, 170, 273, 638, 935, 1394, 2093, 2438, 2465, 4823, 5453, 7973, 11978, 16354, 17963, 34918, 43337, 46943, 62491, 64583, 68266, 71603, 72046, 74347, 75361, 85877, 134458, 148291, 155933, 186235, 188071, 201994, 209933, 280891, 307021, 367081
OFFSET
1,1
COMMENTS
Subsequence of A120944.
LINKS
EXAMPLE
Prime factors of 17963 are 11, 23 and 71 while d(17963) = 8. We have that 17963 - 8 = 17955 and 17955 / (11 - 8) = 5985, 17955 / (23 - 8) = 1197 and 17955 / (71 - 8) = 285.
MAPLE
with (numtheory); P:=proc(q) local a, b, c, i, ok, p, n;
for n from 2 to q do if not isprime(n) then a:=ifactors(n)[2]; ok:=1;
for i from 1 to nops(a) do if a[i][2]>1 or a[i][1]=tau(n) then ok:=0; break;
else if not type((n-tau(n))/(a[i][1]-tau(n)), integer) then ok:=0; break; fi; fi; od; if ok=1 then print(n); fi; fi; od; end: P(10^6);
CROSSREFS
KEYWORD
nonn
AUTHOR
Paolo P. Lava, Aug 20 2013
EXTENSIONS
First term deleted by Paolo P. Lava, Sep 23 2013
STATUS
approved